Download Tutorial 2 - Answer

EKT 241: ELECTROMAGNETIC THEORY
SEM 2 2009/2010
TUTORIAL 2 – ANSWER
Question 1
1. Find the total charge on a circular disk defined by r  a and z  0 if
 s   s 0 r 2 (C/m 2 ) where  s 0 is a constant. The unit of r is in meter.
Solution
Q

a
r 0
2

0
  s 0  0
2
 2s 0
 s 0 r 2 rdrd 

a
0
4 a
r
4
0
 a4 
 2s 0  
4
a 4  s 0

C
2
r 3 dr
Question 2
Find the total charge Q using Gauss’s law for a cylinder of height 3 m and radius 2 m,
given the volume charge density V  2r sin  (nC/m 3 ) .
Solution
Q   2r sin  dV
V

2
2
 
3
r 0  0 z 0
2
2r sin  rdrd dz
2
3
0
0
  2r 2 dr  sin  d  dz
0
2
 2r 3 
2
3

 - cos 0 z 0
 3 0
0C
Question 3
An infinite sheet of charge with uniform surface charge density ρs is located at z = 0 (x-y)
plane and another infinite sheet with density - ρs is located at z = 2m, both in free space.
Determine E in all regions.
Solution
The equation of E for infinite sheet of charge:
For the sheet at z = o
Question 4
Determine the electric potential at the origin in free space due to four charges of 20 C
each located at the corners of a square in the x-y plane and whose center is at origin. The
square has sides of 2 m each.
Solution
The potential due to ONE point charge Q :
P2
V    E  dl (V)
P1
R  - Qr
ˆ 
  (rˆdr )
   
2 
0
4

r
0


r
 Q 


 40 r  0
Q

40 r